Question: Which of the following numbers is a multiple of 13? ${72,82,85,104,105}$
Solution: The multiples of $13$ are $13$ $26$ $39$ $52$ ..... In general, any number that leaves no remainder when divided by $13$ is considered a multiple of $13$ We can start by dividing each of our answer choices by $13$ $72 \div 13 = 5\text{ R }7$ $82 \div 13 = 6\text{ R }4$ $85 \div 13 = 6\text{ R }7$ $104 \div 13 = 8$ $105 \div 13 = 8\text{ R }1$ The only answer choice that leaves no remainder after the division is $104$ $ 8$ $13$ $104$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $104$ $104 = 2\times2\times2\times13 13 = 13$ Therefore the only multiple of $13$ out of our choices is $104$. We can say that $104$ is divisible by $13$.